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Published byJared Greer Modified over 8 years ago

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A coefficient is the number part of a term that includes a variable. Example: 2x 2 is the coefficient x is the variable

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4x + 8x +1 Coefficients are 4 and 8 Constant term 4x and 8x are like terms

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like terms: terms with the same variable or variables, raised to the same power. Like terms can be combined by adding their coefficients. Example: What do you get when you add the fruit shown? Combine like terms + – + By combining apples with apples and oranges with oranges, you get... + 1 apple 3 apples + 2 oranges – 2 apples + 2 oranges + 4 oranges coefficients

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What’s the “same” term mean? ◦ If numbers have a variable, then you can combine only ones that have the same variable ◦ You can also combine numbers that have no variables

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Which numbers are the “same”? 5x, 8y, 9z, 10, 12x, 14z, 7 Same: 5x and 12x Same: 10 and 7 Same: 9z and 14z Same: 8y

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Terms in an algebraic expression are separated by addition or subtraction signs. How many terms are in this expression? The sign in front of each coefficient goes with that term.

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Find the like terms, combine their coefficients... 2x + 3y + 5x + 6y + 12 7x + 9y + 12 Example: Simplify 3x – 3y – 8x – y This is the same as 3x – 3y – 8x – 1y = – 5x – 4y Example: Simplify 2x + 3y + 5x + 6y + 12

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Reorder the terms. Combine like terms.

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Identify like terms. Combine coefficients: 14 – 5 = 9 A. 14a – 5a 9a9a B. 7y + 8 – 3y – 1 + y Identify like terms ; the coefficient of y is 1, because 1y = y. 5y + 7 Combine coefficients: 7 – 3 + 1 = 5 and 8 – 1 = 7

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Combine like terms. Identify like terms; the coefficient of q is 1, because 1q = q. Combine coefficients: 4 – 1 = 3 Identify like terms; the coefficient of c is 1, because 1c = c. 6 3q3q C. 4q – q D. 5c + 8 – 4c – 2 – c Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6

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E. 4m + 9n – 2 4m + 9n – 2 Combine like terms. No like terms. F. 5m – 7m – 8 + 4 -2m – 4

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Remember, to simplify an expression means to perform all possible operations, including combining like terms. In other words, simplify means solve!

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1. 4x + 5y – 2x + 3y 2. 5x + 5y + 2x + 2y 3. 3 + 5x – 4y + 2y – 8x 2x + 8y 7x + 7y 3 – 3x – 2y

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Practice: worksheet

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